{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ITensorMPS\n",
    "using ITensors\n",
    "using Plots\n",
    "using DelimitedFiles\n",
    "using ITensorEntropyTools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find Ground State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After sweep 1 energy=-20.817746085576484  maxlinkdim=10 maxerr=2.06E-03 time=0.021\n",
      "After sweep 2 energy=-20.880837352483518  maxlinkdim=20 maxerr=9.67E-08 time=0.015\n",
      "After sweep 3 energy=-20.88320773063582  maxlinkdim=35 maxerr=9.98E-11 time=0.022\n",
      "After sweep 4 energy=-20.8832119980245  maxlinkdim=30 maxerr=9.95E-11 time=0.020\n",
      "After sweep 5 energy=-20.883211999883134  maxlinkdim=29 maxerr=8.83E-11 time=0.020\n",
      "After sweep 6 energy=-20.88321199988477  maxlinkdim=29 maxerr=8.24E-11 time=0.019\n",
      "After sweep 7 energy=-20.883211999884786  maxlinkdim=29 maxerr=8.24E-11 time=0.018\n",
      "After sweep 8 energy=-20.883211999884807  maxlinkdim=29 maxerr=8.24E-11 time=0.020\n",
      "After sweep 9 energy=-20.883211999884793  maxlinkdim=29 maxerr=8.24E-11 time=0.016\n",
      "After sweep 10 energy=-20.88321199988484  maxlinkdim=29 maxerr=8.24E-11 time=0.016\n",
      "After sweep 11 energy=-20.88321199988479  maxlinkdim=29 maxerr=8.24E-11 time=0.015\n",
      "After sweep 12 energy=-20.883211999884782  maxlinkdim=29 maxerr=8.24E-11 time=0.017\n",
      "After sweep 13 energy=-20.883211999884765  maxlinkdim=29 maxerr=8.24E-11 time=0.016\n",
      "After sweep 14 energy=-20.883211999884782  maxlinkdim=29 maxerr=8.24E-11 time=0.014\n",
      "After sweep 15 energy=-20.88321199988477  maxlinkdim=29 maxerr=8.24E-11 time=0.016\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-20.88321199988477, MPS\n",
       "[1] ((dim=2|id=466|\"Link,l=1\"), (dim=2|id=374|\"S=1/2,Site,n=1\"))\n",
       "[2] ((dim=4|id=256|\"Link,l=2\"), (dim=2|id=450|\"S=1/2,Site,n=2\"), (dim=2|id=466|\"Link,l=1\"))\n",
       "[3] ((dim=2|id=365|\"S=1/2,Site,n=3\"), (dim=8|id=472|\"Link,l=3\"), (dim=4|id=256|\"Link,l=2\"))\n",
       "[4] ((dim=2|id=866|\"S=1/2,Site,n=4\"), (dim=16|id=665|\"Link,l=4\"), (dim=8|id=472|\"Link,l=3\"))\n",
       "[5] ((dim=2|id=435|\"S=1/2,Site,n=5\"), (dim=22|id=697|\"Link,l=5\"), (dim=16|id=665|\"Link,l=4\"))\n",
       "[6] ((dim=2|id=557|\"S=1/2,Site,n=6\"), (dim=27|id=563|\"Link,l=6\"), (dim=22|id=697|\"Link,l=5\"))\n",
       "[7] ((dim=2|id=863|\"S=1/2,Site,n=7\"), (dim=29|id=615|\"Link,l=7\"), (dim=27|id=563|\"Link,l=6\"))\n",
       "[8] ((dim=2|id=922|\"S=1/2,Site,n=8\"), (dim=29|id=995|\"Link,l=8\"), (dim=29|id=615|\"Link,l=7\"))\n",
       "[9] ((dim=2|id=852|\"S=1/2,Site,n=9\"), (dim=29|id=19|\"Link,l=9\"), (dim=29|id=995|\"Link,l=8\"))\n",
       "[10] ((dim=2|id=788|\"S=1/2,Site,n=10\"), (dim=27|id=198|\"Link,l=10\"), (dim=29|id=19|\"Link,l=9\"))\n",
       "[11] ((dim=2|id=675|\"S=1/2,Site,n=11\"), (dim=22|id=717|\"Link,l=11\"), (dim=27|id=198|\"Link,l=10\"))\n",
       "[12] ((dim=2|id=346|\"S=1/2,Site,n=12\"), (dim=16|id=945|\"Link,l=12\"), (dim=22|id=717|\"Link,l=11\"))\n",
       "[13] ((dim=2|id=447|\"S=1/2,Site,n=13\"), (dim=8|id=219|\"Link,l=13\"), (dim=16|id=945|\"Link,l=12\"))\n",
       "[14] ((dim=2|id=19|\"S=1/2,Site,n=14\"), (dim=4|id=271|\"Link,l=14\"), (dim=8|id=219|\"Link,l=13\"))\n",
       "[15] ((dim=2|id=133|\"S=1/2,Site,n=15\"), (dim=2|id=880|\"Link,l=15\"), (dim=4|id=271|\"Link,l=14\"))\n",
       "[16] ((dim=2|id=71|\"S=1/2,Site,n=16\"), (dim=2|id=880|\"Link,l=15\"))\n",
       ")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_s = 16\n",
    "sites = siteinds(\"S=1/2\", N_s)\n",
    "\n",
    "J = 1.0\n",
    "h = 1\n",
    "g = 0.05\n",
    "\n",
    "\n",
    "os = OpSum()\n",
    "for j=1:N_s\n",
    "    if j == N_s\n",
    "        os -= J, \"X\", j, \"X\", 1\n",
    "        os -= g, \"Z\", j, \"Z\", 1\n",
    "    else\n",
    "        os -= J, \"X\", j, \"X\", j+1\n",
    "        os -= g, \"Z\", j, \"Z\", j+1\n",
    "    end\n",
    "    os -= h, \"Z\", j\n",
    "end\n",
    "H = MPO(os, sites)\n",
    "\n",
    "psi0 = randomMPS(sites; linkdims=2^7)\n",
    "\n",
    "nsweeps = 15\n",
    "maxdim = [10,20,100,100,200]\n",
    "cutoff = [1E-10]\n",
    "noise = [1E-6]\n",
    "weight = 50\n",
    "\n",
    "energy0,psi0 = dmrg(H,psi0;nsweeps,maxdim,cutoff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Particle Scattering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "giv_op (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function rz(theta::Float64, i::Int, psi::MPS, cutoff::Float64)\n",
    "    s = siteinds(psi)\n",
    "    z_i = op(\"Z\", s[i])\n",
    "    Op = exp(-1im/2 * theta * z_i)\n",
    "    psi = apply(Op, psi; cutoff)\n",
    "    return psi\n",
    "end\n",
    "\n",
    "function giv_op(theta::Float64, i::Int, j::Int, psi::MPS, cutoff::Float64)\n",
    "    s = siteinds(psi)\n",
    "    x_i = op(\"X\", s[i])\n",
    "    y_i = op(\"Y\", s[i])\n",
    "    x_j = op(\"X\", s[j])\n",
    "    y_j = op(\"Y\", s[j])\n",
    "    Op = x_i * y_j - x_j * y_i\n",
    "    Op = exp(1im * theta / 2 * Op)\n",
    "    psi = apply(Op, psi; cutoff)\n",
    "    return psi\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Vector{Float64}:\n",
       " -0.04452199\n",
       " -0.10805302\n",
       " -0.25917978\n",
       " -0.58569283\n",
       " -1.0800755\n",
       " -1.4472062\n",
       " -1.55743797"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "betas_r = [-2.15984495, -0.78539816,  0.58904862,  1.96349541, -2.94524311,\n",
    "       -1.57079633, -0.19634954,  1.17809725]\n",
    "thetas_r = [-0.04452199, -0.10805302, -0.25917978, -0.58569283, -1.0800755 ,\n",
    "       -1.4472062 , -1.55743797]\n",
    "\n",
    "betas_l = [-2.55254403,  2.35619449,  0.9817477 , -0.39269908, -1.76714587,\n",
    "       -3.14159265,  1.76714587,  0.39269908]\n",
    "thetas_l = [-0.04452199, -0.10805302, -0.25917978, -0.58569283, -1.0800755 ,\n",
    "       -1.4472062 , -1.55743797]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "cutoff = 1E-8\n",
    "\n",
    "# Make an array of 'site' indices\n",
    "s = siteinds(psi0)\n",
    "\n",
    "# State Preparation\n",
    "vacs = [\"0\" for n = 1:N_s]\n",
    "vac = MPS(s, vacs)\n",
    "n_kr = 7\n",
    "n_kl = -n_kr\n",
    "r   = [-Int(N_s/4) + i for i=1:Int(N_s/2)]\n",
    "width_wp = length(r)\n",
    "xr0 = 4\n",
    "xl0 = 12\n",
    "sigma = 3/2\n",
    "\n",
    "\n",
    "init_state = deepcopy(psi0)\n",
    "\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(betas_r[x], x, init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = Int(N_s/2) - x\n",
    "    init_state = giv_op(thetas_r[x], y, y+1, init_state, cutoff)\n",
    "end\n",
    "sm = op(\"X\", s[1]) - 1im * op(\"Y\", s[1])\n",
    "init_state = apply(sm, init_state; cutoff)\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = Int(N_s/2) - x\n",
    "    init_state = giv_op(-thetas_r[y], x, x+1, init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(-betas_r[x], x, init_state, cutoff)\n",
    "end\n",
    "\n",
    "\n",
    "\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(betas_l[x], x+Int(N_s/2), init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = N_s - x\n",
    "    init_state = giv_op(thetas_l[x], y, y+1, init_state, cutoff)\n",
    "end\n",
    "for i in 1:Int(N_s/2)\n",
    "    z = op(\"Z\", s[i])\n",
    "    init_state = apply(z, init_state; cutoff)\n",
    "end\n",
    "sm = op(\"X\", s[Int(N_s/2+1)]) - 1im * op(\"Y\", s[Int(N_s/2+1)])\n",
    "init_state = apply(sm, init_state; cutoff)\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = Int(N_s/2) - x\n",
    "    init_state = giv_op(-thetas_l[y], x+Int(N_s/2), x+Int(N_s/2)+1, init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(-betas_l[x], x+Int(N_s/2), init_state, cutoff)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.14778609267387138, 0.1561014014380392, 0.3124998001126509, 0.5703465766489455, 0.31251651406029535, 0.15610877066250461, 0.14779122569129516, 0.14736931545278614, 0.14778834044561484, 0.15610233713426303, 0.3125003262513082, 0.5703464793735448, 0.3125166044234885, 0.1561084261938216, 0.1477896624792221, 0.14736686631641377]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xp08f9rsBAABgGU0Quri49O3b99y5c6w3AwAAwDb6bYTbt2+PjIwsKysbOnSo2TUI27Rpw0pjAAAAbKj2wrwKhSI6Ojo6OtpsnKIohlsCAABgD00QUhQ1duzYnJycFStWBAQECIXVhiUAAIC9owm5goKCGzduHDhwYMyYMew3BAAAwCaanWXkcrlQKPT29ma/GwAAAJbRBKFCoZgwYcKOHTvY7wYAAIBl9Nv/+vXrt3Tp0ocPHw4bNszBwcH0oTfffJOVxgAAANhAH4TLli0rKCg4ceLEiRMnzB5CEAIAQFNCH4T37t3T6/UstwIAAMA++iB0dnZmuQ8AAACbwPUIAQCA0+jXCNu3b//kyRPah3A9QgAAaErog3Dq1KmlpaXGu2q1OjY29uHDh9hTBgAAmhj6IFy6dKnZiF6vf/PNN6tbTQQAALBTdd1GyOfzP/jgg5iYmJycHEYbAgAAYFM9dpaRSCQUReXl5THXDQAAAMvqGoSZmZkLFiwQi8WBgYGMNgQAAMCmOu01WlFRUVZWJhKJ1q5dK5fL2eoNAACAcXXaa1Qikfj5+Q0aNAiXpwcAgCamrnuNAgAANEk4swwAAHDaC2uE33zzTXFxcc1PWLRoEZP9AAAAsOqFIFy3bl1aWlrNT0AQAgBAU/JCECYlJdFefSklJWXZsmVHjx5t2bIlW40BAACw4YVthM7Ozq4v0mq169at69ev3+XLl9euXfvgwQNbNQoAAMAE+r1GCSElJSVff/31qlWrdDrde++9t3jxYhcXFzY7AwAAYAFNEGo0mq1bt0ZHRxcVFb3xxhvLly/39vZmvzMAAAAWvPDTqFar/f7779u0aTNnzpwBAwbcuXPnu+++QwoCAEAT9sIaYf/+/S9dutS3b9+dO3d27tyZEFJUVGT2BFdXV/a6AwAAYNgLQZidnU0IiYuLGzhwYHVPoCiK6Z4AAABY80IQLlq0qNYD6sG2bt++XV5ebnmd5s2b+/j4WF6nLpKTk8vKymqeU1ZWVuv53Js1a9aqVSvr9QW2l5GRkZ+fb3kdqVQaHBxseZ26yM7OtsplWSUSSVBQEJ+P03vZ3gtBOGfOHFv1AXWRnp7+Urfujq0t/cLrtZVSTXFuxmNrNFWLkpKSkE6dnQM61zyNogiPV+MEvb4iJ6WsFP9Ra1IGDB1RWEEJxFIL65SmJV9PuMpOFr46buL9jDyhTGFhHVXmg1PHj7z88stW6QosUe3hE9AIabVaWbOWRQsvW1roaTZvfV9rdFQ7nU4nkjlYoedKtWielzU6gkakvFJb/I99xMvSq5w6rwnVarVWaalWao22ZPL3JKC3hXVcNg5jrWeoGdbKAQCA0xhcIzx9+vTBgwednJzeeustPz8/s0dTUlL279+flpamUChGjBhRw+45AAAAzGFqjfDgwYPjx48PCgpSq9W9evVSKpVmExISEvLz80NCQpycnCIjI7du3cpQJwAAADVgao1w7dq1a9asmT17NiHk9u3b27ZtmzdvnumE119//fXXXzfcFggEe/bsmTFjBkPNAAAAVIeRNUKNRnPlypXw8HDD3SFDhpw/f766ySqV6uLFi926dWOiEwAAgJpVu0ao0WgSExOzsrLM9msaN25crUXz8vIoimrWrJnhrqenJ+1hN/Hx8SNGjCgpKRkwYMBHH31UXbVHjx4dOXLkypUrhrtisXj9+vVmJ7hRq9UCgaDWxuydWq222gkNKMr02D61Wk2ItU6VULWy1dR6PCLYSsO+g9b6PFOElJeXm348KIrminINqkyZVaa9Vl2DSlMVFRWN5yNdVlZGUVTTO65RLBYLhbX89kn/8Llz5954443Hjx9XfaguH1yxWEwIMSaoRqORSCRVp3Xv3j0lJSU3NzcqKioqKurbb7+lrebm5tapU6fXXnvNcJfP57u5uRkWYVTdIpoYs1dtER7P9F9MLBYTUuNxfPUpXaWy1XDhXbZTDfsOWu0zR4hYLDZtgFfzcan1qMwzq8y3UmXC44lEosbzkdZqtRKJpOkFYV1eEX0Qzpw5UyqV/v777+3bt681S6vy8PAQi8WZmZmG9bbMzEzaK/oKhULDVQ8//PDD119/vbogdHZ2bt269fjx42tYokAg4MIaoUAgsNbX21CN9ra9VIZGpYHfQet9nvl8/osNMFaZwZ5tyfAONr0grAuakFMqlY8ePTp58uTQoUMbVpTP548ePfqXX37p1KmTRqM5cOBAdHQ0IUStVp89e3bIkCESiaS4uNjJyckw/+LFi/7+/g1+DQAAAA1GE4QSiUQoFDo6OlpSd/ny5UOGDElOTk5LS2vevPnYsWMJIXl5eSNHjszOzvb29p48eXJBQYGvr29aWlpGRsb+/fstWRwAAEDD0AShQqGYNGnSjh07wsLCGlw3JCTk3r1758+fd3Z27tu3r2H1v2XLlklJSR4eHoSQffv2JSQkZGdnN2/ePDQ0VCq19GSDAAAADUC//W/EiBHz589PS0sbMWKEp6en6UN12WvUwMXFZfTo0aYjIpHIcJlDQohYLO7d29KT9QEAAFiIPgjfe++9vLy8I0eOHDlyxOwhXI8QAACaEvogjI+P1+l0LLcCAADAPvogxOVPAQCAI2o6RvDWrVuJiYkZGRne3t4hISGhoaGstQUAAMAO+iAsKyubMmXKgQMHTAcHDhz466+/uru7s9IYAAAAG+hPIjBv3rzDhw9HR0ffvHmzsLAwOTn5008/TUhIwAUiAACgiaFZI9RoNDt27Fi3bp3xwklubm4dOnTw8/ObOHFiXl5e8+bN2W0SAACAKTRrhAUFBWq1uur51YYNG0ZRVHp6OiuNAQAAsIEmCF1cXIRCYVJSktm4YcTs+HoAAAC7RhOEcrl85MiR77zzzu7duw2XUtLr9cePH58xY0bPnj1xZAUAADQl9DvLfPPNNz4+PhMmTJDJZC1atJDJZCNGjODxeDt27GC5PwAAAEbRHz7h7e197dq1AwcOxMXF5ebmuru7h4WFjRs3Ti6Xs9wfAAAAo6o9oF4sFo8fP77my+ECAADYOy5ejBgAAMDoeRDu3r3b29t748aNhJDOnTt7V8N2rQIAAFjf859G/f39x48f37FjR0LIa6+9VlJSYruuAAAAWPI8CHv27NmzZ0/D7RUrVtioHwAAAFbRbyNcuXJlWlqa2WB6evrixYuZbwkAAIA99EG4adOmrKwss8GsrKx169Yx3xIAAAB76rHXaFFRkZOTE3OtAAAAsO+F4wivXr165swZQohKpYqJiTl//rzxoaKiot9++61z585sNwgAAMCkF4LwwoULxq2A33zzjelD7u7uISEhX375JXutAQAAMO+Fn0bnzZtHURRFUc2bN4+Li6NMFBQUnDt37qWXXrJVowAAAEygP8XavXv3FAoFy60AAACwjz4InZ2dWe4DAADAJuj3Gq2srPz444+DgoKkUinvRSz3BwAAwCj6NcIlS5Zs2LBh5syZcrncyckpLCzs2LFj9+/fnzdvHsv9AQAAMIp+jXDLli0rV6787rvvOnXq1Lt379WrVyckJEycODEpKYnl/gAAABhFs0ZYWFhYVFQ0cuRIQohAICgrKyOE8Pn8ZcuWtWrVKjs7u0WLFmy3CQAAwAyaNUKxWEwI0ev1hBAvL6+MjAzDuIuLC0VROTk5bPYHAADAKJogdHR0bNmy5Z07dwghPXv2PHHixOXLlzUazerVqwUCgb+/P+tNAgAAMIV+Z5lJkyadO3duwoQJo0aNCgkJ6d27t2F84cKFbm5uLLYHAADALPog/PTTTw03+Hz+2bNnjx49+vjx465duw4aNIjF3gAAABhHH4SmpFJpREQEC60AAACwr9og1Gq1R48evX79elZWlpeXV0hIyKuvviqVStlsDgAAgGn0QZiZmTl69OjExESBQODm5lZUVKTVagMCAg4dOtSxY0eWWwQAAGAO/QH106ZNy8zM3LNnj1qtzs/PLy8vP3bsmF6vj4iIMBxWAQAA0DTQBKFSqTx79uy33347btw4kUhECBEIBMOHD9+5c+fdu3eTk5NZbxIAAIApNEFIURQhJDg42Gw8JCSE/O9AewAAgKaBJgjd3d1DQ0MPHTpkNn7o0CEfHx9sIwQAgKaEfmeZVatWTZ06NT09PSIiwsvLq6Cg4OjRo5s3b96wYUN6erphjoeHh6OjI4utAgAAWB99EE6bNi0/P3/Tpk2bNm0yHZ80aZLx9g8//DBr1ixmuwMAAGAYfRD+8MMP5eXlNT8zNDSUgX4AAABYRR+Eo0ePZrkPAAAAm6A/jhAAAIAj6NcIX3/99aKiItqH/vjjDyb7AQAAYFXtJ90mhBQUFNy9e1cqlWK7IAAANDH0Qbhnzx6zkdzc3MjIyJEjRzLfEgAAAHvquo3Qy8vryy+/XLJkSXFxMaMNAQAAsKkeO8v4+vqWl5c/fPiwjvN1Ot3FixfPnTtXUVFBO+Hp06exsbEXLlxQqVR1bwMAAMCK6rSN0GDLli2EkFatWtVlcllZ2ZAhQzQajaOjY1ZWVmxsrLe3t+mEbdu2vffee506ddLpdA8ePDhw4EDfvn3r1ToAAIDl6rrX6KNHj1JSUiZMmODu7l6Xuj/99BOfz79y5YpAIJgyZcr69ev/85//mE7o2bNnamqqq6srIWTZsmULFiy4fPlyQ18FAABAA9X1p9E+ffrExMTExMTUcf7+/fsnTpwoEAgIIVOnTt23b5/ZhI4dOxpSkBASHBz89OnTOlYGAACworruNVpfGRkZfn5+htt+fn5ZWVl6vZ7Pp8ldnU63cePGCRMmVFequLg4IyPD2JJAIBg1apThQolGer2eC9eH0uv1hotkWasa7W17qQyNSgO/g1b7OFdtwJrfFIY+eBRFNZ6PdFP9K0qbO2bqsY2wXjQajTGrxGKxTqerrKyUSCRm0yiKioqKIoQsWbKkulL5+fn37t0znvtUIBD06tXLzc3NdE5FRYVZNDZJ1e121BAUZXo62YqKCuv94aha2Wp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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "magz = expect(init_state, \"Z\")\n",
    "occs = [(1 - magz[n])/2 for n=1:N_s]\n",
    "println(occs)\n",
    "\n",
    "sites = [n for n=1:N_s]\n",
    "plot(bar(sites, occs; label=\"TEBD\"), xlabel=\"site (s)\", ylabel=\"Occupation Number\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14736686631641377"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "occs[16]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "96-element Vector{ITensor}:\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=374|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=374|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=374|\"S=1/2,Site,n=1\")'\n",
       "Dim 2: (dim=2|id=374|\"S=1/2,Site,n=1\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=374|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=374|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "Dim 2: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=866|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=866|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "Dim 2: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=866|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=866|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=866|\"S=1/2,Site,n=4\")\n",
       "Dim 2: (dim=2|id=435|\"S=1/2,Site,n=5\")\n",
       "Dim 3: (dim=2|id=866|\"S=1/2,Site,n=4\")'\n",
       "Dim 4: (dim=2|id=435|\"S=1/2,Site,n=5\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ⋮\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=866|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=866|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "Dim 2: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=866|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=866|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "Dim 2: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=365|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=365|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=374|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=374|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=374|\"S=1/2,Site,n=1\")'\n",
       "Dim 2: (dim=2|id=374|\"S=1/2,Site,n=1\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=374|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=450|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=374|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=450|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make Time-Evolution Circuit\n",
    "tau = 0.05\n",
    "N_t = 120\n",
    "\n",
    "gates = ITensor[]\n",
    "for j in 1:N_s\n",
    "    s1 = s[j]\n",
    "    if j == N_s\n",
    "        s2 = s[1]\n",
    "    else\n",
    "        s2 = s[j+1]\n",
    "    end\n",
    "    \n",
    "    x1 = op(\"X\", s1)\n",
    "    x2 = op(\"X\", s2)\n",
    "\n",
    "    hxx = - J * x1 * x2\n",
    "\n",
    "    Gj = exp(-1im * tau * hxx/2)\n",
    "\n",
    "    push!(gates, Gj)\n",
    "\n",
    "    hz = - h * op(\"Z\", s1)\n",
    "    Gj = exp(-1im * tau * hz/2)\n",
    "    push!(gates, Gj)\n",
    "\n",
    "    z1 = op(\"Z\", s1)\n",
    "    z2 = op(\"Z\", s2)\n",
    "\n",
    "    hzz = -g * z1 * z2\n",
    "\n",
    "    Gj = exp(1im * tau * hzz/2)\n",
    "    push!(gates, Gj)\n",
    "end\n",
    "\n",
    "# Include gates in reverse order too\n",
    "# (N,N-1),(N-1,N-2),...\n",
    "append!(gates, reverse(gates))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273352)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273346)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273353)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273352)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273352)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273346)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273352)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273355)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273353)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273353)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273353)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273355)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.30015725927335)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300157259273348)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n"
     ]
    }
   ],
   "source": [
    "function entropy_von_neumann(psi::MPS, b::Int)\n",
    "  s = siteinds(psi)  \n",
    "  orthogonalize!(psi, b)\n",
    "  _,S = svd(psi[b], (linkind(psi, b-1), s[b]))\n",
    "  SvN = 0.0\n",
    "  for n in 1:dim(S, 1)\n",
    "    p = S[n,n]^2\n",
    "    SvN -= p * log(p)\n",
    "  end\n",
    "  return SvN\n",
    "end\n",
    "\n",
    "# Compute and print <Sz> at each time step\n",
    "# then apply the gates to go to the next time\n",
    "# maxdim = Int(2^(N_s/2))\n",
    "maxdim = 40\n",
    "occs = []\n",
    "EEs = []\n",
    "dims = []\n",
    "ttotal = N_t * tau\n",
    "state = init_state\n",
    "for t in 0:tau:ttotal\n",
    "    # println(\"Pass 1\")\n",
    "    Sz = expect(state, \"Z\")\n",
    "    occ = [(1 - Sz[n])/2 for n=1:N_s]\n",
    "    push!(occs, occ)\n",
    "\n",
    "    EE = []\n",
    "    for j in 2:N_s-1\n",
    "      ee = ee_region(state, 1:j)\n",
    "      push!(EE, ee)\n",
    "    end\n",
    "    push!(EEs, EE)\n",
    "    \n",
    "    bond_dim = maxlinkdim(state)\n",
    "    push!(dims, bond_dim)\n",
    "    t ≈ ttotal && break\n",
    "\n",
    "    state = apply(gates, state; cutoff, maxdim)\n",
    "    normalize!(state)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sites = [n for n=1:N_s]\n",
    "# for p in 1:length(occs)\n",
    "#     if (p - 1) % 10 == 0\n",
    "#         plt = plot(bar(sites, occs[p]; label=\"TEBD\"); ylims= (0,0.6), xlabel=\"site\")\n",
    "#         png(plt, \"Plots/plt\" * string(p) * \".png\")\n",
    "#     end\n",
    "# end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_times = zeros((N_t+1))\n",
    "plot_occs = zeros((N_t+1, N_s))\n",
    "for i in 1:N_t+1\n",
    "    plot_times[i] = (i - 1) * tau\n",
    "    for j in 1:N_s\n",
    "        plot_occs[i,j] = occs[i][j]\n",
    "    end\n",
    "end\n",
    "\n",
    "plot_sites = zeros((N_s))\n",
    "for i in 1:N_s\n",
    "    plot_sites[i] = i\n",
    "end\n",
    "\n",
    "heatmap(plot_sites, plot_times, plot_occs, xlabel=\"site (s)\", ylabel=\"time t\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "title = \"Data/\"\n",
    "title *= \"ising-approx-occs-N_s\" * string(N_s)\n",
    "title *= \"-J\" * string(J)\n",
    "title *= \"-h\" * string(h)\n",
    "title *= \"-g\" * string(g)\n",
    "title *= \"-width\" * string(sigma)\n",
    "title *= \"-dt\" * string(tau) * \".txt\"\n",
    "writedlm(title, plot_occs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Data/ising-approx-occs-N_s16-J1.0-h1-g0.05-width1.5-dt0.05.txt\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "EEs_mat = stack(EEs, dims=1)\n",
    "title = \"Data/\"\n",
    "title *= \"ising-approx-EEs-N_s\" * string(N_s)\n",
    "title *= \"-J\" * string(J)\n",
    "title *= \"-h\" * string(h)\n",
    "title *= \"-g\" * string(g)\n",
    "title *= \"-width\" * string(sigma)\n",
    "title *= \"-dt\" * string(tau) * \".txt\"\n",
    "writedlm(title, EEs_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Data/ising-approx-EEs-N_s16-J1.0-h1-g0.05-width1.5-dt0.05.txt\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.12.1",
   "language": "julia",
   "name": "julia-1.12"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
